Eccentric asking to hide (8)
I believe the answer is:
goatskin
'hide' is the definition.
(I know that goatskin is a type of hide)
'eccentric asking to' is the wordplay.
'eccentric' indicates an anagram.
'asking'+'to'='askingto'
'askingto' anagrammed gives 'GOATSKIN'.
(Other definitions for goatskin that I've seen before include "Hide Billy or Nanny" , "Billy's hide?" , "Type of leather - a song kit (anag)" , "Leather - wine holder of old" , "Leather from nanny or billy?" .)